Mathematical Modelling of Transient Processes in a 10-storey Building Represented as Heaviside Functions

Abstract

The purpose of the scientific work is to consider the problems of mathematical modeling of seismic safety of a tenstorey building with a base in the form of an elastic halfplane under unsteady wave influences. The problem of modeling problems of the transition period is an urgent fundamental and
applied scientific problem. An algorithm and a set of programs
for solving linear planar two-dimensional problems have been
developed. The algorithmic language Fortran-90 was used in
the development of the software package. An explicit twolayer
finite element scheme is obtained.
To assess the reliability of the developed methodology, algorithm and software package, the problem of the impact of a pulse in the form of three halfcycles of a sinusoid on an elastic halfplane was solved. A system of equations consisting of 8016008 unknowns is solved. The problem of the effect of a plane longitudinal elastic wave in the form of a Heaviside function on a tenstorey building with a base is considered. A system of equations consisting of 16202276 unknowns is solved. Contour stresses and stress tensor components are obtained in the characteristic areas of the problem under study. Based on the conducted studies, the following conclusions can be drawn: the elastic contour stress on the faces of the building is almost a mirror image of one another, that is, antisymmetric; bending waves mainly prevail during seismic action.